> If you have a set with two binary operations, then a monoid isn't the correct abstraction. I guess my point is that even if I used "the correct abstraction"

> If you have a set with two binary operations, then a monoid isn't the correct abstraction. I guess my point is that even if I used "the correct abstraction" here, meaning a ring or something, then the whole newtype setup still makes it annoying for me to split off one operation and feed it into a function expecting a monoid: the way that fold and friends work is much more natural, just taking a starting value 1 and an operation * for example, rather than some kind of "Multiplicative" newtype or whatever. In general I see a lot of the abstract algebra type towers in Haskell and Purescript as being unhelpful, and making a huge assumption that (for example) there will rarely be two monoid instances on a type. In reality in abstract algebra we use tons of different operations on the same objects all the time, and I really just want to define those operations and then be able to use them.